Efficient data structures for the factor periodicity problem

Authors:
Tomasz Kociumaka;Jakub Radoszewski;Wojciech Rytter;Tomasz Waleń
Affiliations:
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland;Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland;Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland,Faculty of Mathematics and Computer Science, Copernicus University, Toruń, Poland;Laboratory of Bioinformatics and Protein Engineering, International Institute of Molecular and Cell Biology in Warsaw, Poland,Faculty of Mathematics, Informatics and Mechanics, University of Warsa ...
Venue:
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
Year:
2012

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Extracting powers and periods in a word from its runs structure

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Abstract

We present several efficient data structures for answering queries related to periods in words. For a given word w of length n the Period Query given a factor of w (represented by an interval) returns its shortest period and a compact representation of all periods. Several algorithmic solutions are proposed that balance the data structure space (ranging from O(n) to O(nlogn)), and the query time complexity (ranging from O(log1+εn) to O(logn)).